Asperity Deformation Research Articles

A Novel Normal Contact Stiffness Model of Bi-Fractal Surface Joints

The contact stiffness of the mechanical joint usually becomes the weakest part of the stiffness for the whole machinery equipment, which is one of the important parameters affecting the dynamic characteristics of the engineering machinery. Based on the three-dimensional Weierstrass–Mandelbrot (WM) function, the novel normal contact stiffness model of the joint with the bi-fractal surface is proposed, which comprehensively considers the effects of elastoplastic deformation of asperity and friction factor. The effect of various parameters (fractal dimension, scaling parameter, material parameter, friction factor) on the normal contact stiffness of the joint is analyzed by numerical simulation. The normal contact stiffness of the joint increases with an increase in the fractal dimension, normal load, and material properties and decreases with an increase in the scaling parameter. Meanwhile, the fractal parameters of the equivalent rough surface of the joint are calculated by the structural function method. The experimental results show that when the load is between 14 and 38 N∙m, the error of the model is within 20%. The normal contact stiffness model of the bi-fractal surface joint can provide a theoretical basis for the analysis of the dynamic characteristics of the whole machine at the design stage.

Experimental and finite element analysis of surface asperity geometry during the running-in phase of rolling contact

This paper presents the experimental and finite element analysis of surface asperity geometry during the running-in phase of rolling contact. Previous research efforts typically relied on simulating various shapes of asperity geometry to elucidate rough surface characteristics. However, this approximation did not accurately represent the actual surface asperities. In this study, a rolling contact rig was fabricated, and periodic surface scans were utilized to track the deformation of roller surface asperities. The experimental findings reveal a notable 69% reduction in surface roughness throughout the running-in phase, alongside showcasing the deformation of asperity geometry. Subsequently, a simulation model is developed using data derived from these experiments. Stress analysis conducted on individual and multiple asperities illustrates a decrease in contact stress over time, indicating a transition in contact behavior from plastic to elastic. Furthermore, simulations involving multiple asperities demonstrate an expansion in contact length as roughness diminishes with increasing cycles. Initially, only the highest peaks of asperities make contact, resulting in elevated contact stress. However, as rolling cycles progress, a greater number of asperities come into contact, leading to a more uniform distribution of load. Notably, the more prominent asperities endure significant contact stress and deformation compared to their smaller counterparts.

Influence of Lubricated Rolling/Sliding Tribotesting on Hydrogen Trapping in 100Cr6 Bearing Steel

As hydrogen reduces the fatigue life of 100Cr6 bearing steel significantly, extensive research on the interaction of hydrogen with 100Cr6 is necessary. This study investigated the influence of rolling/sliding tribotesting performed on a micro-pitting-rig on the hydrogen absorption and trapping behaviour of 100Cr6 bearing steel. Thermal desorption mass spectrometry was used to compare the hydrogen desorption spectra of 100Cr6 samples after tribological tests and static heated oil-immersion tests to untested reference samples. The approach was chosen to further understand the influence of both microstructural deformation as well as steel-oil contact on the hydrogen absorption and trapping behaviour of 100Cr6. The tribological test showed a stable friction behaviour and mild wear which was dominated by local plastic deformation of surface asperities. Despite the mild wear, a change in de-trapping temperatures was found for tribotested samples compared to oil-immersed and untested reference samples. This finding indicates that even mild tribotesting conditions alter the hydrogen trapping behaviour of 100Cr6 bearing steel.

Electrical detachment of triboelectrically charged bumpy particles from rough surfaces

The detachment of bumpy particles from smooth and rough surfaces through electrostatic fields was studied. The Johnson–Kendall–Roberts (JKR) adhesion model for elastic interface deformations was used to account for the individual bump adhesion, including the electrostatic forces. It was assumed that the elastic deformation of asperities determines the real contact area, and the effect of topographic properties of substrates was included in the analysis. For a fixed charge per unit mass, the Coulomb, the image, the dielectrophoretic, and the polarization forces acting on the particle in the presence of an imposed electric field were evaluated. The electrostatic detachment of bumpy toner particles for various applied electrostatic fields was studied. The triboelectric charges were concentrated on the hemispherical bumps, and the critical electric field strength needed to detach charged particles from surfaces with varying roughness levels was evaluated. It was shown that the particle charge, surface roughness, and the number of bumps significantly affect the removal of particles from surfaces. For higher charges (∼5 × 10−15 C ), decreasing the number of bumps from 22 to 14 and the roughness parameter from 0.83 to 0.77 approximately doubled the detachment field needed to remove 8.3 μ m polystyrene (PSL) particles from the aluminum oxide substrate. The model predictions are compared with the available experimental data, and good agreement was observed. The study’s findings predicting the electric field needed for charged particle removal could lead to more efficient copiers and electrostatic cleaning devices.

In situ SEM side observation of asperity behavior during sliding contact

The performance and evolution characteristics of the friction interface are crucial for the design optimization of material friction and wear, as well as the revelation of the mechanism of seismic sliding motion. To understand the friction behavior of rough surfaces, it is essential to understand the physical process of interaction among asperities. However, visualizing the contact of asperities is challenging because materials are typically opaque, and the dimensions of asperities are usually in the micron range. This study developed an in-situ scanning electron microscope friction device and a micro speckle fabrication method to measure the strain field of regular asperities from the side, and synchronously measure the macroscopic friction coefficient. In-situ friction experiments were conducted on brass and silicon materials. The results indicate that directly correlating the friction coefficient with the deformation and failure images of asperities can effectively explain the evolution process and differences in friction coefficient for the two materials, validating the performance of the device. Different failure modes of asperities were observed, including severe plastic deformation in brass asperities and fracture-producing large particles in silicon asperities. The critical transition of asperity failure modes in the experiments was analyzed based on a theoretical model. The phase diagram of asperity failure modes and friction coefficient evolution was plotted, providing potential explanation for the evolution of friction coefficient in friction experiments on randomly rough surfaces. The developed device in this study can be used for non-transparent materials and helps reveal the microscopic mechanisms behind experimental phenomena.

The Environmental and Economic Importance of Mixed and Boundary Friction

One route to reducing global CO2 emissions is to improve the energy efficiency of machines. Even small improvements in efficiency can be valuable, especially in cases where an efficiency improvement can be realized over many millions of newly produced machines. For example, conventional passenger car combustion engines are being downsized (and also downspeeded). Increasingly, they are running on lower-viscosity engine lubricants (such as SAE 0W-20 or lower viscosity grades) and often also have stop–start systems fitted (to prevent engine idling when the vehicle is stopped). Some of these changes result in higher levels of mixed and boundary friction, and so accurate estimation of mixed/boundary friction losses is becoming of increased importance, for both estimating friction losses and wear volumes. Traditional approaches to estimating mixed/boundary friction, which employ real area of contact modelling, and assumptions such as the elastic deformation of asperities, are widely used, but recent experimental data suggest that some of these approaches underestimate mixed/boundary friction losses. In this paper, a discussion of the issues involved in reliably estimating mixed/boundary friction losses in machine elements is undertaken, highlighting where the key uncertainties lie. Mixed/boundary lubrication losses in passenger car and heavy-duty internal combustion engines are then estimated and compared with published data, and a detailed description of how friction is related to fuel consumption in these vehicles, on standard fuel economy driving cycles, is given. Knowing the amount of fuel needed to overcome mixed/boundary friction in these vehicles enables reliable estimates to be made of both the financial costs of mixed/boundary lubrication for today’s vehicles and their associated CO2 emissions, and annual estimates are reported to be approximately USD 290 billion with CO2 emissions of 480 million tonnes.

Frictional evolution process and stability properties of Longmaxi shale under fluid injection

The frictional stability of rocks is fundamental in controlling the instability and activation of faults. Given the strong correlation between seismic events in the Sichuan Basin of China and hydraulic fracturing for shale gas extraction, we conducted a series of velocity-stepping friction experiments with Longmaxi shale from the Changning shale gas extraction block under fluid injection. The experimental results indicate that the frictional process of Longmaxi shale can be divided into four distinct stages and the effective normal stress can demonstrate the influence of injection pressure. Additionally, the phenomenon of a decreasing friction coefficient μ with increasing effective normal stress can be explained by the frictional adhesion theory and a competitive mechanism between the deformation of asperities and microscopic dilatant slip. As the injection pressure increases, the friction state of Longmaxi shale transitions from velocity-strengthening to velocity-weakening, which is beneficial for potential seismic slip. After friction, the fracture surface experiences wear, and the surface morphology of the left and right parts exhibits a symmetrical distribution. With increasing effective normal stress, the morphological evolution of fractures becomes more prominent, which is related to the variation in the effective contact area. Based on the experimental results, we propose that the uneven distribution of fluid pressure on the Longmaxi shale fracture may also contribute to the transformation of frictional stability. When studying the frictional properties of rocks under fluid injection, it is also necessary to focus on the evolution of fluid pressure distribution on the fracture surface during the frictional process.

Effect of squamous textured SiC on the dry-sliding tribological properties of graphite asperities

The graphite rough morphology influences the operating performance of the sealing surface. Texturing silicon carbide surfaces can considerably improve the tribological characteristics of sealing surface. Herein, a fractal model was established to study the contact and tribological characteristics of graphite asperities, and the pin-on-disk wear tests were conducted to investigate the influence of squamous texture on graphite asperities under dry-sliding condition. Results indicated that reducing the graphite surface roughness decreases the contact area to decrease the friction coefficient. The squamous texture increases the deformation and contact area of graphite asperities. But the wear debris collection of the squamous texture prevents the adhesive wear, and the microcutting effect promotes the formation of graphite transfer film on the silicon carbide surface. Therefore, the squamous texture has the low friction coefficient and excellent worn morphology. Especially, under the high load of 80 N, combining the textured silicon carbide with the optimal graphite surface roughness of 0.14 μm exhibits a synergistic anti-friction effect that the friction coefficient reduced by 19%.

Loading condition monitoring of high-strength bolt connections based on physics-guided deep learning of acoustic emission data

Aiming at life-cycle condition monitoring of high-strength bolt connections, a physics-guided deep learning framework integrating supervised and unsupervised learning was developed to diagnose manifold damage mechanisms and identify different loading stages using acoustic emission (AE) data. For data preprocessing, empirical wavelet transform (EWT) was introduced to provide adaptive and compact time–frequency representations of AE signals where diverse damage mechanisms behaved with various energy distributions. A convolutional neural network (CNN) model was first built to extract damage-related features from multiscale EWT matrices of AE data labeled by the loading stages I, II-III, and IV that were redefined according to their dominant damage mechanisms. Stage I (static friction) could be identified directly, which was characterized by the distinct damage mechanism of plastic deformation of asperities. After that, Gaussian mixture model (GMM) was applied to cluster the extracted feature vectors of AE data induced by multiple damage mechanisms overlapped among stages II (sliding), III (confined), and IV (failure). With the help of Bayesian information criterion (BIC), three damage mechanisms were recognized, including abrasive wear of asperities, adhesive wear of asperities, and plastic deformation and cracking of screw, which were validated by their EWT components. Finally, based on the proportions of AE data corresponding to diverse damage mechanisms, the rules were established for identifying the four loading stages of high-strength bolt connections. Experimental results demonstrated that the three-class CNN model with data labeled by the redefined loading stages achieved a higher accuracy than the four-class CNN model with data straightforwardly labeled by the original loading stages. Not only the critical damage states of static friction failure (looseness) and shear failure, but the four loading stages of high-strength bolt connections and their overlapped damage mechanisms were successfully identified by the physics-guided CNN-GMM framework.

Development of interactive friction model for machining considering the instantaneous interfacial characteristics

In this article, the transient and complex tribological characteristics of machining interfaces have been considered for developing a friction model. The interfacial characteristics – a condition where process parameters are in fluctuation rather than being constant – are identified. In an investigation of coated carbide tool wear in machining AISI H13 steel, the dominant wear mechanisms were identified as the abrasion, adhesion, and asperity deformation. Considering the complex loading, transient tribological behaviours, and observed wear mechanisms in machining, an interactive friction model is developed based on the mutually interactive nature of wear-and-friction. The evolution of the coefficient of friction with machining time is considered with different stages of tool wear. The adjusting capability of the developed model with respect to the complex loading is explored. The value of this research is to discover a unique behaviour at interfaces, additionally to identify the transient tribological conditions including wear mechanisms, and for the first time, to develop the interactive friction model for machining that adds scientific contribution to the domain of machining tribology.

Two-dimensional contact of asperities to multi-stage contact between curved fractal surfaces based on attitude angle

Based on the attitude angle of asperities, a multi-stage model is established for the curved contact between fractal surfaces. The asperity exhibits deviation between its axis and the global normal, thereby the attitude angle of asperity occurs. Asperity deformation depending on attitude angle is derived at length scale. Attitude angle also leads to a two-dimensional load of asperity, presenting double origins of plastic mode and corresponding critical length scales. With increasing load, the critical length scale varies, and the contact processes four stages incorporating the effects of attitude angle. The contact characteristics of each stage are calculated, and verification by experimental data is provided. This work illustrates the substantive characteristics of curved contact due to the asperity attitude.

A numerical study on the impact of lubricant rheology and surface topography on heavily loaded non-conformal contacts

The increasing requirement of high-power density (power throughput/ weight) in modern day machines lead to thin film lubrication condition in various machine components (rolling element bearings, gears, cams, etc,) due to severe loading conditions. Surface roughness features and lubricant rheology plays a vital role in thin film lubrication, and significantly affects the lubrication performance and lifetime of machine components. The present work demonstrates surface topography and lubricant rheology effects on the traction coefficient for heavily loaded non-conformal contacts. The load-sharing concept considering elastic-plastic deformation of asperities, and Carreau shear-thinning rheological model is employed to describe the dry rough contacts and non-Newtonian behavior of lubricant. An influence of surface topography parameters such as roughness, skewness, kurtosis, and pattern ratio on the traction coefficient is discussed. From results, it is found that among different surface topographies, negatively skewed surfaces having isotropic surface pattern exhibit minimum traction coefficient. The load share function and the critical rolling speed are determined for various surface topographies which provides further insights into the surface topography effect on traction coefficient. The findings of present study are noteworthy as they provide a theoretical basis for an assessment of the lubrication performance of heavily loaded non-conformal contacts.

Contacting Micro Asperity of a Deformable Surface

Abstract Deterministic contact modeling based on half-space theories has satisfied a wide range of applications. However, the half-space theories themselves do not involve shape effects of roughness on Green’s functions/influence coefficients; in deterministic rough-surface contact analyses, the roughness is considered in gap function. This approach can be called the “roughness simplification.” One needs to answer two questions about the validity of the roughness simplification: How appropriate is the roughness simplification in modeling rough-surface contacts? How accurately can the commonly included contact-plasticity behavior be captured under the roughness simplification? This work utilized a double-scale representation of an asperity—a microscopic deformable asperity stacked on a deformable half-space, to obtain their combined contact responses in both elastic and plastic regimes. The deformation and contact behaviors of asperities thus configured were obtained with finite element analysis (FEA) and rough-surface half-space contact solvers. Three stages of asperity contact were discovered: the Hertzian stage, the single-region elastoplastic stage, and the two-region elastoplastic stage where the surrounding base material also takes part in the contact. The comparisons of contact deformation and pressure results from both the finite element analysis and half-space contact solvers support the validity of the half-space theories with the roughness simplification for various ellipsoid-shape asperities with circular-bases in both elastic and elastoplastic rough-surface asperity modeling. The research also reveals that when significant plastic deformations occur, asperities with different aspect ratios can bear different maximum elastoplastic contact pressures.

A Mixed Lubrication Deterministic Model of an Elastic Support Water-Lubricated Tilting Pad Thrust Bearing

In order to study the effect of surface roughness on lubrication performance of an elastic support water-lubricated tilting pad thrust bearing, a mixed lubrication (ML) deterministic model is hereby presented based on a unified Reynolds equation model. This very model incorporates the elastic–plastic deformation of asperities and polymer matrix of the thrust pad, as well as the elastic deformation of the rubber support. The randomly distributed surface roughness of the thrust pad is generated by a mathematical model and shares the same distribution characteristics as the measured surface roughness. The Greenwood and Williamson asperity contact model and thin plate deformation model are combined to solve the asperities contact stress and deformation. Meanwhile, the bearing ML performance is compared with the results calculated by a thermohydrodynamic (THD) lubrication model and a thermo-elasto-hydrodynamic (TEHD) lubrication model, while the film thickness is also compared with measurements. The results show that the water film thickness calculated by the ML model is smaller than that by the THD model and the TEHD model, but the water film temperature is higher. The roughness has a great influence on the contact area ratio and the lubrication state, but little effect on the average film thickness. A higher roughness indicates a higher rotational speed required for the bearing to achieve full hydrodynamic lubrication. The film thickness calculated by the mixed lubrication model is closer to the measured results. Overall, it is proved that the mixed lubrication model can more accurately predict the lubrication performance of bearings. Compared to the thin plate deformation model, the elastic deformation simulation based on the half-infinite space model severely overestimates the elastic deformation of the pad surface, making it unsuitable for calculating the elastic deformation of the polymer matrix of the thrust pad under contact force or water film pressure. This ML deterministic model provides an effective means for high-precision prediction of the lubrication performance of the elastic supported water-lubricated thrust bearings coupled with multi-layer soft materials.

Numerical and experimental study of the preload induced period-1 and chaotic vibration of a rotor system considering contact effects

Contact effects are one of the primary nonlinear sources of vibrations in the gas turbine rotor systems. Specifically, the nonlinear stiffness between the disk interface from the contact effects has an important influence on the vibration characteristics. In this study, a contact model that accounts for the elastoplastic deformation of asperity is established based on the contact theory. To improve the macroscopic contact model of the bolted structure, we integrate the tested morphology results and modified the skewed distribution function. Subsequently, a dynamic model of the rod fastened rotor-bearing system that incorporates the nonlinear oil film force is established. The influence of the preload on the vibration characteristics of the rotor bearing system is analyzed. The results demonstrate that the improved contact model accurately describes the distribution of asperities on rough surface. The contact effects weaken the rotor lateral stiffness to a certain extent. According to the numerical results and experimental results, it can be found that changes in preload significantly affects the occurrence conditions from periodic vibration to chaotic vibration, a higher preload is conducive to maintaining the stable period-1 motion state at high speed. Additionally, as the preload is decreased, the speed range with obvious periodic-doubling frequencies gradually increases and the amplitude of vibration response decreases. This work provides a practical guidance for the dynamic design and preload adjustment of gas turbine rod-fastened rotor considering contact effects.

Theoretical and Experimental Study on Normal Contact Stiffness of Plane Joint Surfaces With Surface Texturing

Effects of surface texturing on normal contact stiffness have been investigated by experiments in previous research studies; however, there are relatively few theoretical models in this regard. This article aims to investigate the influence of surface texturing on the normal contact stiffness in theory and experiment. In the present research, a rough surface with surface texturing is divided into two parts, the textured zone and the remaining zone, and their theoretical models of normal contact stiffness are established respectively, considering surface morphology and material properties. For the textured zone, microtextures are modeled theoretically based on the three-dimensional topographic data obtained via a laser profilometer. For the remaining zone, the surface topography is characterized based on fractal theory, and a calculation model is established considering the elastoplastic deformation of surface asperities. In the experiment, the normal contact stiffness of specimens is obtained through the self-developed experimental platform. The proposed theoretical model is appropriate through the comparison of test results and theoretical predictions. The research results show that the effect of surface texture on the contact stiffness is related to the surface roughness, Sa. For the joint surfaces with Sa > 2.69 μm, the normal contact stiffness can be effectively increased through proper surface texturing.

Case study of advanced processed OFHC copper by dry sliding wear test

The wear behaviour of copper material processed by ECAP (Equal Channel Angular Pressing) and orbital forging (OF) is presented in this study. Dry sliding wear tests were carried out for the wear behaviour of the investigated system. Oxygen-free high thermal conductivity (OFHC) copper was used for testing. The new combination of metal forming processes was used because of ease of fabrication. Additionally, wear rate, friction coefficient and wears mechanisms were observed. The friction resistance is caused by the destruction of the adhesion between surface asperities in metal friction. Moreover, increased asperity interactions connected with wear particle entrapment gradually increase the friction coefficient. These results show the metal forming process's positive influence in reducing interfacial adhesion and asperity deformation. Finally, the combinations of newly used advanced processing demonstrated excellent wear characteristics of copper.

A quantitative analysis of double-sided surface waviness on TEHL line contacts

In this paper, the effects of double-sided surface waviness on Thermo-Elastohydrodynamic Lubrication (TEHL) in line contacts are investigated deterministically through numerical simulations. The effects of surface amplitude, wavelength, relative position, and slide-to-roll ratio have been studied. The classic approach, which consists of an equivalent deformable body with superimposed surface waviness, is critically evaluated and compared to results from full two-body simulations. Under the investigated conditions, the equivalent and two-body approaches show about 17%, 21%, and 26% deviations in maximum pressure, temperature, and friction, respectively. It is demonstrated that the fundamental cause of the observed deviations, which results in a phase shift that cannot be described by the equivalent geometry, is the tangential elastic deformation of surface asperities.

A multi-asperity adhesive contact model for catheter and vascular artery contact in endovascular surgery.

Contact behaviors of medical devices, such as guidewires and catheters, are critical in endovascular surgeries. In this work, a new method to predict adhesive contact force between catheter and vascular artery is presented. Multi-asperity adhesion on the surface of vascular artery, deformation of asperity and deformation of vascular substrate are all considered. The single asperity behavior is described with Johnson-Kendall-Roberts (JKR) contact model. The multi-asperity behavior is based on Greenwood-Williamson (GW) asperity model. Vascular substrate is considered as elastic bulk substrate and its deformation is determined with Hertzian pressure from asperity on a circular region on the elastic half space. The model shows that the deformation of vascular substrate accounts for the majority of the total contact deformation and significantly affects the predicted contact force. The model is verified with published experimental data. The comparison shows that the model produces very accurate prediction of contact force between catheter and vascular artery when the contact force is compressive. Parametric analysis based on asperity topography is carried out. The analysis shows that the diameter of the circular region of the interface between asperity and vascular substrate has more significant effect on the estimation of contact force than the radius of asperity. Further validation of prediction accuracy of the model under experiment is needed.

Experimental estimation of thermal contact conductance across pressed copper–copper contacts at cryogenic-temperatures

• Present experimental work presents a valuable database of TCC in cryogenics. • Reports systematic estimates of TCC for copper contacts on which data are scarce. • Effects of broad temperature, pressure, roughness on TCC are covered in vacuum. • Anomalous TCC trend at low temperature is correlated to thermo-physical properties. • Proposes generalized empirical correlations of TCC with temperature and pressure. The accurate estimation of thermal contact conductance (TCC) is a fundamental need towards the optimal design of any cryogen-free conduction-based cooling systems, which routinely utilizes mechanically pressed components of bare copper to form the heat conduction path. There exists a dearth of databases and reliable correlation for TCC between bare copper contacts for such applications. Present work is an experimental study, which has been performed systematically to address the requirement of design engineers for such applications. A novel experimental setup has been made to carry out axial heat transfer experiments between copper contacts under a varying set of temperature and pressure parameters of 50 to 300 K and 0.5 to 8 MPa, respectively. The surface roughness at the contact between copper specimens varied between 0.8 and 10 μ m . The TCC has shown a non-linear variation with temperature in the 50 to 300 K. The temperature-dependent thermophysical properties, nature of asperities deformation, and surface topography characterization were considered in analyzing the results. This effectively helps in dealing with the coupled nature of the TCC problem and thus enhances the accuracy, reliability, and scope of the present study performed at sub-ambient ranges under a varying set of selected parameters. The TCC results have also been compared with theoretical model predictions, and the improvements needed in them are highlighted. Finally, an empirical correlation of the reduced dimensionless TCC with dimensionless temperature and dimensionless pressure has been proposed, which covers a wide deformation range of the asperities, temperature, and surface roughness than existing models in the literature. The proposed correlation consistently explains the non-linear dependence of TCC with temperature and pressure and provides a direct means to the design engineers for the TCC estimation at cryogenic temperatures.